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Consider a regression model where y is explained by two regressors x1 and x2, i.e. a regression of the form yi = x1i*BETA1 + x2i*BETA2 + ui (1) where i = 1,...,N observations are available.
- Rewrite the model in matrix notation and derive the formula for the OLS estimator.
- Show formally that if two regressors are orthogonal, i.e.SUM(x1i*x2i) = 0, the values obtained for the coefficients BETA1 and BETA2 by estimating (1) are identical to the coefficients obtained by performing an OLS regression of y on only x1 respectively by performing an OLS regression of y on only x2.
- Show that due to the orthogonality of the regressors also the estimated coefficients BETA(hat)1 and BETA(hat)2 are uncorrelated, i.e. show that cov(BETA(hat)1, BETA(hat)2) = 0.
The following survey questions have been established for a medical errors and patient safety business research paper:
Construct a 95% Confidence interval for diffrence between the two populations. At the alpha equals .10 level of significance, can the firm conclude that Chicago households buy more online than Milwaukee.
At times we can generate a regression equation to explain outcomes. For example, an employee's salary can often be explained by their pay grade, appraisal rating, education level, etc.
Suppose that 1% of all the students seeking treatment at the school infirmary have mono. Of the students who do have mono, 90% complain of a sore throat. Of the students who do not have mono, 30% also have sore throats.
The amount ($1.00, $5.00, $10.00, $25.00, or $50.00) promised to each person was determined by randomization. For each person who was sent one of the surveys, The value of the X2 test statistic for testing the hypothesis
the transportation safety authority tsa has developed a new test to detect large amounts of liquid in luggage bags.
In his management information systems textbook, Professor David Kroenke raises an interesting point:“If 98% of our market has Internet access, do we have a responsibility to provide non-Internet materials to that other 2%?Suppose that 98% of the cust..
From past experience, an automobile insurance company knows that a given automobile will suffer a total loss with probability .02, a 50% loss with probability .08, or a 25% loss with probability .15 during a year.
Can you determine the exact number of days that it rained? Can you conclude anything about the number of days that it rained? Explain.
According to an internet posting, 80% of adults enjoy drinking beer. Choose a group of 3 adults at random. The probability that none of them enjoy drinking beer is:
Determine a 95% confidence interval for true mean cost to repair this type of car.
One measure of the overall sampling error in the entire distribution of sample means is the
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